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JEE Main202224 Jun 2022Morning ShiftMathematicsComplex NumberActual

Let A = z ∈ C : 1 ⩽ z - 1 + i ⩽ 2 and B = z ∈ A : z - 1 - i = 1 . Then, B

Options

  1. Ais an empty set
  2. Bcontains exactly two elements
  3. Ccontains exactly three elements
  4. Dis an infinite set

Correct answer

D. is an infinite set

Step-by-step solution

z - 1 + i = 1   &   z - 1 + i = 2 represents two concentric circles with centre 1 , 1 . z - 1 - i = 1 represents a circle with centre 1 , - 1 and radius 1 A represents the region between the concentric circles with centre 1 , 1 Set B contains all points on minor arc P Q of the circle z - 1 - i = 1 . Hence, B has infinite elements.

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